scholarly journals Critical exponent for the semilinear wave equation with time-dependent damping

2012 ◽  
Vol 32 (12) ◽  
pp. 4307-4320 ◽  
Author(s):  
Jian Zhai ◽  
Kenji Nishihara ◽  
Jiayun Lin
Keyword(s):  
Wave Equation ◽  
Critical Exponent ◽  
Time Dependent ◽  
Semilinear Wave Equation

A Modified Test Function Method for Damped Wave Equations

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Marcello D’Abbicco ◽  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Critical Exponent ◽  
Function Method ◽  
Wave Equations ◽  
Time Dependent ◽  
Small Data ◽  
Test Function ◽  
Test Function Method ◽  
Modified Test

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

Fujita’s Exponent for a Semilinear Wave Equation with Linear Damping

2002 ◽  
Vol 2 (1) ◽  
Author(s):  
Mokhtar Kirane ◽  
Mahmoud Qafsaoui
Keyword(s):  
Wave Equation ◽  
Critical Exponent ◽  
Semilinear Wave Equation ◽  
Linear Damping

AbstractWe discuss the critical exponent problem for the semilinear wave equation with linear dampingu

scholarly journals Scattering for critical wave equations with variable coefficients

2021 ◽  
pp. 1-19
Author(s):  
Shi-Zhuo Looi ◽  
Mihai Tohaneanu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Energy Decay ◽  
Time Dependent ◽  
Linear Wave ◽  
Decay Estimates ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Semilinear Wave Equation

Abstract We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$ , but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$ .

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